(a) Write 9.1% as a decimal,
(b) Write 0.216 as a percentage
The Correct Answer and Explanation is:
To solve the given problems, we need to convert between percentages and decimals.
(a) Writing 9.1% as a Decimal
To convert a percentage to a decimal, you divide the percentage by 100. This is because the term “percent” means “per hundred.” Here are the steps:
- Start with the percentage: 9.1%.
- Divide by 100:
[
9.1 \div 100 = 0.091
]
So, 9.1% as a decimal is 0.091.
(b) Writing 0.216 as a Percentage
To convert a decimal to a percentage, you multiply the decimal by 100. Again, this is based on the definition of percent, which represents a part of 100. Here are the steps:
- Start with the decimal: 0.216.
- Multiply by 100:
[
0.216 \times 100 = 21.6
]
Thus, 0.216 as a percentage is 21.6%.
Explanation
Understanding the conversion between decimals and percentages is essential for various mathematical applications, including finance, statistics, and everyday calculations. A percentage represents a ratio or fraction out of 100, making it an intuitive way to express proportions. For example, if you say that a product has a discount of 9.1%, it implies that for every 100 units of currency, the discount is 9.1 units.
When converting percentages to decimals, dividing by 100 simplifies the calculation. This conversion is particularly useful when you need to perform arithmetic operations, such as addition or multiplication, with percentages. For instance, if you are calculating a 9.1% sales tax on an item costing $50, you would first convert 9.1% to its decimal form (0.091) and then multiply it by 50 to find the tax amount.
Conversely, converting decimals to percentages is crucial when you want to express a part of a whole in a more relatable format. For example, saying that 0.216 represents 21.6% helps people understand the proportion relative to 100%. In summary, mastering these conversions aids in clear communication of quantitative information and enhances mathematical literacy.